Multilayer foam-film composite structures are known, and the structures of U.S. Pat. Nos. 3,557,265 and 5,215,691 are exemplary. These structures can be made by various processes, including lamination and co-extrusion, and uses in various applications, including mailing envelopes, shipping sacks, stand-up pouches, labels, thermoformed packaging and tamper-evident packaging. However, various properties of these structures have room for improvement, particularly the properties of toughness, tear resistance and puncture resistance.